Integer factorization using integer programming...

Let z be a positive integer. The task is to determine whether there exist integers x,y >= 2 such that z = xy. The catch is that this must be done using an integer programming model, i.e. something of the form:

[; \text{min}\;c^T x\\\quad\text{s.t.} Ax=b\\\quad x\in\mathbb{Z_+} ;]

I'm not asking anyone to do my homework for me, but I've been working on this for hours. Basically, the objective function isn't important; it's an issue of feasibility. The professor's hint was to consider the input number z in binary and find a correspondence between binary multiplication and the logical AND operation but I'm just not seeing it. Any ideas?